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1 and the imaginary unit

From the definition of the imaginary unit i follows immediately

i 4 = 1

and that is somewhat surprising.

 


Explanation

The complex number i has only an imaginary part, and has no real value. But you can perform calculations with it, as

i 0 = 1 ,    i 1 = i ,    i 2 = – 1 ,   i 3 = – i
i 4 = 1 ,   i 5 = i ,     i 6 = – 1 ,   i 7 = – i

and so on. With great regularity the real numbers 1 and –1 occur.

 


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